The realization space is
  [1   1   0   0   1   1                     0                   x2^2 - x2                   x2^2 - x2                1    1]
  [1   0   1   0   1   0                x2 - 1   x1*x2^2 + x2^2 - 2*x2 + 1   x1*x2^2 + x2^2 - 2*x2 + 1               x1   x1]
  [0   0   0   1   1   1   x1*x2^2 - x2^2 + x2                 x2^3 - x2^2                     x1*x2^3   x1*x2 - x2 + 1   x2]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal with 2 generators
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1*x2 - 2*x2 + 1, x1, x1*x2 + x2^2 - 2*x2 + 1, x1^2*x2^2 - 2*x1*x2^2 + x2 - 1, x1^2*x2^2 - x1*x2^2 - x2^2 + 2*x2 - 1, x1*x2 - x2 + 1, x2, x1*x2^2 - x2 + 1, x2 - 1, x1^2*x2 - x1*x2 + x1 - x2 + 1, x1^2*x2^2 - 2*x1*x2^2 + x1*x2 + x2 - 1, x1^2*x2^2 - x1*x2^2 + x1*x2 - x2^2 + 2*x2 - 1, x1 + x2 - 1, x1 - x2, x1*x2 - 2*x2 + 2, x1^2*x2^3 - 2*x1*x2^3 + x1*x2^2 + x1*x2 + x2^3 - 2*x2 + 1, x1^2*x2^2 + 2*x1*x2^3 - 5*x1*x2^2 + 3*x1*x2 - 3*x2^3 + 8*x2^2 - 7*x2 + 2, x1^2*x2 - 2*x1*x2 + 2*x1 + x2 - 1, x1*x2 + x1 - x2, x1*x2^2 + x2^2 - 2*x2 + 1, x1^2*x2^3 - 2*x1*x2^3 + x1*x2^2 + x1*x2 + x2^2 - 2*x2 + 1, x1^2*x2^3 - x1*x2^3 + x1*x2 - x2^3 + 4*x2^2 - 5*x2 + 2, x1*x2^3 + x1*x2^2 - x2 + 1, x1^2*x2^3 - x1*x2^2 + x1*x2 - 2*x2^3 + 5*x2^2 - 4*x2 + 1, x1^2*x2^3 - x1*x2^2 + x1*x2 - 2*x2^3 + 6*x2^2 - 6*x2 + 2, x1*x2^2 + x2^3 - x2^2 - x2 + 1, x1*x2^2 - x2^3 + 2*x2^2 - 2*x2 + 1, x1*x2^2 - x2^2 + 2*x2 - 1, x1*x2^2 - x2^2 + 1]